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Search: id:A136197
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| A136197 |
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Fixed points or cycle values for sequences of the form s(k+1)=sopfr(2s(k)+1), with sopfr=A001414, and any s(1). |
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+0
4
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OFFSET
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1,1
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COMMENT
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A136136 starts with s(1)=1 and ends in 10 as fixed point.
For s(1) from 1 to 10000 either (a) the sequence converges to 10, the fixed point; or (b) it cycles - between 14, 29, 59 and 24.
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EXAMPLE
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s(1)=1; ... s(6)=12; s(7)=sopfr(2*12+1)=5+5=10; s(8)=sopfr(2*10+1)=3+7=10
s(1)=1 leads to 10 as fixed point.
s(1)=2; ... s(7)=24; s(8)=14; s(9)=29; s(10)=59; s(11)=24
s(1)=2 leads to the cycle (24 14 29 59).
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MATHEMATICA
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sopfr = Function[x, Plus @@ Map[Times @@ # &, FactorInteger[x]]]; Union[Table[NestList[sopfr[2# + 1] &, s0, 100][[ -1]], {s0, 1, 10000}]]
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CROSSREFS
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Cf. A136136.
Adjacent sequences: A136194 A136195 A136196 this_sequence A136198 A136199 A136200
Sequence in context: A136802 A084278 A069207 this_sequence A071620 A053690 A031028
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KEYWORD
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nonn
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AUTHOR
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Carlos Alves (cjsalves(AT)gmail.com), Dec 20 2007
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